A method for calculating vertical stress of stope floor and application thereof

Abstract

The application provides a kind of stope floor vertical stress calculation method, method is: when upper working face mining, mining area surrounding rock reaches a new stress equilibrium state, under the new stress equilibrium state, the stress of floor under the mining area and coal pillar will appear obvious asymmetry, at this time, the stress of any point M of stope floor surrounding rock is composed of initial in-situ stress and additional stress, the above working face advancing direction is the positive direction of x axis, the vertical x direction downward is the positive direction of z axis to establish a rectangular coordinate system, the coordinate point of any point M of stope floor surrounding rock in rectangular coordinate system is M (x, z), a stope floor mechanical model is established, and the model is used for calculation.The application obtains the distribution expression of stope floor vertical stress according to the superposition of stope floor additional stress and initial in-situ stress, aims to provide relevant theoretical reference for the problem of dynamic pressure influence of lower coal seam mining under close distance coal seam, so as to realize the safe and efficient development of coal mine.

Description

Technical Field

[0001] This invention belongs to the field of coal mining technology, specifically relating to a method for calculating the vertical stress of the bottom plate of a mining area and its application. Background Technology

[0002] Studying the vertical stress of the floor at different depths in mining areas can improve the safety of coal mining, reduce personnel and equipment losses, and create safe production conditions for the mine. In close-range coal seam mining, the roof of the lower coal seam is damaged by the concentrated stress of the upper coal seam wall, which alters the integrity and physical and mechanical properties of the surrounding rock in the lower coal seam roadway. This makes the working face highly susceptible to roof collapse, large deformation of the surrounding rock in the retreat roadway, difficulty in support, and significant mine pressure manifestation during lower coal seam mining. Therefore, studying the depth and law of vertical stress transmission from the upper coal seam during downward mining in close-range coal seams, and the influence of this transmission on the pre-existing dynamic pressure of the lower coal seam, as well as identifying stress concentration areas, is of great significance.

[0003] The excavation of the underground mining floor disrupts the original stress equilibrium, causing rock mass movement and stress redistribution within the rock mass. This process leads to movement or deformation of the surrounding rock mass and support equipment. Therefore, it is necessary to study and analyze the vertical stress of the mining floor. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating the vertical stress of the bottom plate of a mining area, which addresses the shortcomings of the prior art. This method uses theoretical analysis to divide the stress structure of the upper coal seam mining area and studies the stress distribution and variation law of the bottom plate of the mining area, thus providing a reliable theoretical basis for coal mining.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the vertical stress of the bottom plate of a mining area, characterized by comprising the following steps:

[0006] S101. When the upper working face is being mined, the surrounding rock in the mining area reaches a new stress equilibrium state. Under this new stress equilibrium state, the stress in the floor below the mining area and coal pillar will exhibit significant asymmetry. The non-uniform distribution of stress will lead to a significant change in the vertical stress of the floor surrounding rock. A rectangular coordinate system is established with the upper working face advancing in the positive x-axis direction and the vertical x-direction downwards in the positive z-axis direction. The spatial stress of the mining floor is decomposed into two parts: the initial original rock stress and the additional stress caused by engineering disturbance. The stress at any point in the floor surrounding rock can be decomposed into the superposition of the initial original rock stress and the additional stress. The mining floor surrounding rock mass is considered as a semi-infinite ideal elastic body. The additional stress belongs to a stress field that does not consider the influence of its own weight. Therefore, the stress change of the floor can be solved using the planar semi-infinite body method. The stress distribution under the mining floor is obtained by superimposing the additional stress value with the initial original rock stress value. The superposition calculation formula is as follows:

[0007] σ z =σ z Equation (1) +γH

[0008] In the formula: γ is the unit weight of the overburden in the mining area, H represents the burial depth of the coal seam being mined, and the additional vertical stress at any point M(x,z) below the floor of the mining area is σ. z 、,σ z This indicates the total vertical stress at the bottom plate of the mining area after the end of mining and the redistribution of stress in the surrounding rock.

[0009] S102, According to equation (1), when the additional stress value reaches its maximum, σ z Taking (K-1)γH, when the additional stress value reaches its minimum, σ z Take -γH, where the vertical stress of the bottom plate is 0, and K is the maximum stress concentration factor. The stress growth distribution range of the mining floor mechanical model is divided into three regions: I (additional stress influence region directly below the mining area, length a); II (vertical stress and additional stress rise region affected by engineering disturbance, length b); and III (solid coal support stress peak restored to the initial original rock stress region, length c). When the elastic semi-infinite plane is subjected to a vertical force of intensity q(t) in the (-a, b+c) section, the force caused by a micro-element dt at point t in the (-a, b+c) section is q(t)dt. The expression for the additional stress caused by q(t) at a point M(x,z) within the semi-infinite plane is:

[0010]

[0011] Integral operation on equation (2)

[0012]

[0013] The stress generated at point M by the additional stress in regions I, II, and III is calculated by equation (3). The stress expression under the single-sided stope floor is obtained by superimposing the vertical stresses of each region at point M.

[0014]

[0015] In equation (4), σ z1 σ represents the additional stress in the surrounding rock below region I. z2 , representing the additional stress in the surrounding rock below region II, σ z3 The stress at point M represents the additional stress in the surrounding rock below region III. The stress at any point M below the stope floor is obtained by adding the additional stress at point M in regions I, II, and III to the initial original rock stress.

[0016] σ z =σ z′1+σ z ′2+σ z Equation (5) is ′3+γH

[0017] Substituting equation (4) into equation (5) yields the vertical stress σ at point M(x,z) below the bottom plate of the mining area. z

[0018]

[0019] In addition, the present invention also provides an application of a method for calculating the vertical stress of the stope floor, comprising the following steps:

[0020] S201, the vertical stress σ of the mining floor plate z The calculation formula was written in Origin C language, and the variables in the formula were simplified during the writing process;

[0021] S202. Using the Origin custom fitting function manager, the vertical stress σ of the prepared mining floor plate is calculated. z Compile the code to obtain the compiled function;

[0022] S203. Input the specific parameters into the compiled function;

[0023] S204. Substitute the specific parameters input in S203 into σ. z The calculation formula for σ is plotted. z The curve graph shows the distribution pattern of vertical stress in the bottom plate of the mining area;

[0024] S205, σ drawn according to S204 z The curve graph visually obtains the magnitude of vertical stress at different depths below the mining floor. Based on the magnitude of vertical stress at different depths below the mining floor, roadways at different locations in the lower coal seam are reinforced with support.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] This invention employs theoretical analysis to divide the stress structure of the upper coal seam mining area and studies the stress distribution and variation law of the mining area floor. By establishing a mechanical model of the mining area floor, the calculation formula for the vertical stress of the mining area floor is derived, and the distribution law of the vertical stress of the mining area floor is analyzed. Based on the superposition of the additional stress of the mining area floor and the initial original rock stress, the distribution expression of the vertical stress of the mining area floor is obtained. This invention aims to provide relevant theoretical reference for the problem of the influence of dynamic pressure on the lower coal seam in close-range coal seam mining, thereby achieving safe and efficient coal mining.

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0028] Figure 1 This is a stress decomposition diagram of the stope in this invention. a is a schematic diagram of the stress distribution of the stope floor, b is a schematic diagram of the initial original rock stress distribution, and c is a schematic diagram of the additional stress distribution.

[0029] Figure 2 This is a schematic diagram showing the division of regions I, II, and III in this invention.

[0030] Figure 3 This is a simplified schematic diagram of the additional stress on the bottom plate of the mining area in this invention.

[0031] Figure 4 This is a graph showing the vertical stress distribution of the mining floor at different depths in this invention.

[0032] Figure 5 This is a schematic diagram of the model used for simulation and comparison in this embodiment.

[0033] Figure 6 This is a vertical stress distribution diagram obtained during the simulation comparison in this embodiment. Detailed Implementation

[0034] Example 1

[0035] This embodiment describes a method for calculating the vertical stress of the bottom plate of a mining area, including the following steps:

[0036] S101. When the upper working face is being mined, the surrounding rock in the mining area reaches a new stress equilibrium state. Under this new stress equilibrium state, the stress in the floor below the coal pillar and in the mining area will exhibit significant asymmetry. This non-uniform stress distribution will lead to a significant change in the vertical stress of the surrounding rock. A rectangular coordinate system is established with the upper working face advancing in the positive x-axis direction and the vertical x-direction downwards in the positive z-axis direction. The spatial stress of the mining floor is decomposed into two parts: the initial original rock stress and the additional stress caused by engineering disturbance. The spatial stress of the mining floor is as follows: Figure 1 As shown in figure a, the initial original rock stress distribution is as follows: Figure 1 As shown in b, the distribution of additional stress is as follows: Figure 1 As shown in c. The stress at any point in the surrounding rock of the stope floor can be decomposed into the superposition of the initial original rock stress and the additional stress. Considering the surrounding rock mass of the stope floor as a semi-infinite ideal elastic body, the additional stress belongs to a stress field that does not consider the influence of its own weight. Therefore, the stress change of the floor can be solved using the planar semi-infinite body method. The stress distribution under the stope floor is obtained by superimposing the additional stress value with the initial original rock stress value. The superposition calculation formula is:

[0037] σ z =σ z Equation (1) +γH

[0038] In the formula: γ is the unit weight of the overburden in the mining area, H represents the burial depth of the coal seam being mined, and the additional vertical stress at any point M(x,z) below the floor of the mining area is σ. z 、,σ z This indicates the total vertical stress at the bottom plate of the mining area after the end of mining and the redistribution of stress in the surrounding rock.

[0039] S102, Figure 2 P and Q represent the maximum additional stress values ​​of the solid coal and the floor beneath the mining area, respectively, where P is the point of maximum vertical stress. According to equation (1), when the additional stress value reaches its maximum, σ z Taking (K-1)γH, when the additional stress value reaches its minimum, σ z Let -γH be taken, at which point the vertical stress of the floor is 0, where K is the maximum stress concentration factor. The stress growth distribution range of the mechanical model of the stope floor is divided into three regions in sequence: I, the additional stress influence region directly below the stope with a length of a; II, the vertical stress and its additional stress rise region affected by engineering disturbance with a length of b; and III, the region where the peak stress of the solid coal support is restored to the initial original rock stress with a length of c.

[0040] S103. When an elastic semi-infinite planar body is subjected to a vertical force of intensity q(t) in the segment (-a, b+c), as follows: Figure 3 The force induced by a differential element dt at point t in the (-a, b+c) region of the elastic planar body shown is q(t)dt. The expression for the additional stress induced by q(t) at a point M(x,z) within the semi-infinite planar body is:

[0041]

[0042] Integral operation on equation (2)

[0043]

[0044] The stress generated at point M by the additional stress in regions I, II, and III is calculated using equation (3). The stress expression under the single-sided stope floor is obtained by superimposing the vertical stresses at point M from each region.

[0045]

[0046] In equation (4), σ z1 σ represents the additional stress in the surrounding rock below region I. z2 , representing the additional stress in the surrounding rock below region II, σ z3 The stress at point M represents the additional stress in the surrounding rock below region III. The stress at any point M below the stope floor is obtained by adding the additional stress at point M in regions I, II, and III to the initial original rock stress.

[0047] σ z =σz ′1+σ z ′2+σ z Equation (5) is ′3+γH

[0048] Substituting equation (4) into equation (5) yields the vertical stress σ at point M(x,z) below the bottom plate of the mining area. z

[0049]

[0050] Example 2

[0051] This embodiment illustrates an application of a method for calculating the vertical stress of a mining floor, including the following steps:

[0052] S201, the vertical stress σ of the mining floor plate z The calculation formula was written in Origin C language. To simplify the writing process, the variables in the formula were simplified, and the simplified variable correspondence is shown in Table 1.

[0053] Table 1 Simplified Correspondence Table of Variables

[0054] M l H x a z b c K

[0055] Vertical stress σ of the stope floor z The calculation formula is written as follows

[0056] M=((l*H) / pi)*(((a+x) / a)*(((x*z) / ((x^2)+(z^2)))-((x+a)*z) / ((x+a)^2+z^2 )+atan(x / z)-atan((x+a) / z))+((bK*x) / b)*((((xb)*z) / ((xb)^2+z^2))-((x*z) / ((x^2)+(z^2)))+atan((xb) / z)-atan(x / z))+((1-K)*((b+cx) / c))*((((xbc)*z ) / ((xbc)^2+z^2))-((xb)*z) / ((xb)^2+z^2)+atan((xbc) / z)-atan((xb) / z))+pi)

[0057] S202. Using the Origin custom fitting function manager, the vertical stress σ of the prepared mining floor plate is calculated. z Compile the code to obtain the compiled function;

[0058] S203. Input the specific parameters into the compiled function: a = 22m, b = 3m, c = 14m, K = 2.4, (γH)p = 2.52MPa; p represents the pressure generated on the bottom surface of the foundation by the self-weight of the foundation and the backfill soil on it.

[0059] S204. Draw σ based on the specific parameters input in S203. z Curve graph Figure 4 Substituting these values ​​into the above formula yields the distribution law of vertical stress in the bottom plate of the mining area;

[0060] S205, σ drawn according to S204 z The curve graph visually obtains the magnitude of vertical stress at different depths below the mining floor. Based on the magnitude of vertical stress at different depths below the mining floor, roadways at different locations in the lower coal seam are reinforced with support.

[0061] To verify the accuracy and practical value of Example 2, simulation studies were conducted using the mechanical analysis software FLAC3D developed by Itasca. Modeling was performed using six-sided bricks as the basic structural units, with the model dimensions being 500m × 200m × 110m, containing 14 rock layers. The working face dimensions were 300m × 160m × 4m, with 40m coal pillars left on each side. Excavation began from the left side of the model along the x-direction. Step pressures ranging from 0 to 3.77MPa were applied along the x and y directions at the model boundaries to simulate the horizontal stress at different depths. The gravity was set to 9.8N / kg. The model had fixed boundaries. After initial stress calculation and equilibrium, the working face was excavated in one go, with an excavation step of 20m. The constitutive relation of the model adopted the Mohr-Coulomb criterion. The modeling process is as follows: Figure 5 As shown:

[0062] After the model is completed, the vertical stress data of the rock strata 30m below the coal seam working face is extracted. The vertical stress distribution characteristics of the model are plotted using Origin. As can be seen from the figure, the stress peak will advance with the advancement of the working face. Based on the relationship between stress magnitude and distance, the distribution characteristics of vertical stress can be quantitatively analyzed.

[0063] The numerical simulation results show that the peak vertical stress in the model is located approximately 30m in front of the working face, which corresponds to the vertical stress distribution obtained using Formula 6 (z = 30m). Figure 6 approximate.

[0064] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Any simple modifications, alterations, and equivalent changes made to the above embodiments based on the inventive essence shall still fall within the protection scope of the present invention.

Claims

1. A method for calculating the vertical stress of the bottom plate of a stope, characterized in that, Includes the following steps: When the working face is being mined, the surrounding rock in the mining area reaches a new stress equilibrium state. Under the new stress equilibrium state, the stress of the bottom plate under the mining area and the coal pillar will show obvious asymmetry. At this time, the stress of any point M in the surrounding rock of the mining area bottom plate is composed of the initial original rock stress and the additional stress. A rectangular coordinate system is established with the working face advancing direction as the positive x-axis and the vertical x-direction downward as the positive z-axis. The coordinate point of any point M in the surrounding rock of the mining area bottom plate in the rectangular coordinate system is M(x,z). A mechanical model of the mining area bottom plate is established. The formula for calculating the vertical stress of the stope floor is obtained from the mechanical model of the stope floor. In the formula, γ represents the unit weight of the overlying strata in the mining area, H represents the burial depth of the coal seam being mined, and σ z The total vertical stress of the bottom plate of the mining area after the end of mining and the redistribution of stress in the surrounding rock is represented by: a is the length of the additional stress influence area directly below the mining area; b is the length of the vertical stress affected by the engineering disturbance and the length of the additional stress rise area; c is the length of the area where the peak value of the solid coal support stress recovers to the initial original rock stress; and K is the maximum stress concentration factor.

2. The method for calculating the vertical stress of the stope floor as described in claim 1, characterized in that, When establishing the mechanical model of the stope floor, the surrounding rock mass is considered as a semi-infinite ideal elastic body. The stress variation of the floor is solved using the planar semi-infinite body method. The stress distribution under the stope floor is obtained by superimposing the additional stress value with the initial original rock stress value. The superposition calculation formula is as follows: σ z =σ z , +γH Equation (1) In the formula: σ z , represents the additional vertical stress at any point M(x,z) below the bottom plate of the mining area; The stress growth distribution range of the mining floor mechanical model is divided into three regions: I, the additional stress influence region directly below the mining floor (length a); II, the vertical stress and additional stress rise region affected by engineering disturbances (length b); and III, the region where the peak stress of the solid coal support is restored to the initial original rock stress (length c). When the elastic semi-infinite plane is subjected to a vertical force of intensity q(t) in the (-a, b+c) segment, the force caused by a micro-element dt at point t in the (-a, b+c) segment is q(t)dt. The expression for the additional stress caused by q(t) at a point M(x,z) within the semi-infinite plane is then obtained. Integral operation on equation (2) The stress generated at point M by the additional stress in regions I, II, and III is calculated by equation (3). The stress expression under the single-sided stope floor is obtained by superimposing the vertical stresses of each region at point M. In equation (4), σ z1 σ represents the additional stress in the surrounding rock below region I. z2 , representing the additional stress in the surrounding rock below region II, σ z3 The stress at point M represents the additional stress in the surrounding rock below region III. The stress at any point M below the stope floor is obtained by adding the additional stress at point M in regions I, II, and III to the initial original rock stress. s z =s z ′1+σ z ′2+σ z ′3+γH formula(5) Substituting equation (4) into equation (5) yields the vertical stress σ at point M(x,z) below the bottom plate of the mining area. z 3. An application of a method for calculating the vertical stress of a mining area floor as described in any one of claims 1 and 2, comprising the following steps: S201, the vertical stress σ of the mining floor plate z The calculation formula was written in Origin C language, and the variables in the formula were simplified during the writing process; S202. Using the Origin custom fitting function manager, the vertical stress σ of the prepared mining floor plate is calculated. z Compile the code to obtain the compiled function; S203. Input the specific parameters into the compiled function; S204. Draw σ based on the specific parameters input in S203. z The curve graph is obtained by substituting the specific parameters input in S203 into σ. z The calculation formula for σ is plotted. z The curve graph shows the distribution pattern of vertical stress in the bottom plate of the mining area; S205, σ drawn according to S204 z The curve graph visually obtains the magnitude of vertical stress at different depths below the mining floor. Based on the magnitude of vertical stress at different depths below the mining floor, roadways at different locations in the lower coal seam are reinforced with support.

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